416 PROFESSOR KELLAND ON FRESNEL'S FORMULiE FOR THE 



Or (i_R)^_2i^-T^-2i^'=-ila-T,) 



sin (p sm (p J JVl 



~~fyL ■ ^ ^' ^y means of (3). 



Now y =^ 2 (<^ r + ^ 5/ ) sin K X' 



S g^ + a^'-2g/ . . 

 = - 2 r sm O ar^ 



F S SSa;'^;/ _,„s.t . .^ 

 -J= +f — ^ — ^ smfby 



and the quantities on the right hand sides of these two equations, are the co- 

 efficients respectively of terms which result from forces arising from a motion 

 perpendicular to that of transmission, but extending only half through the system. 

 There are, in fact, two terms aiising fi-om this cause, the one corresponding to the 

 vibratory motion each, and having its value & in both, and the other the term in 

 question. 



Hence we conclude, that 



M_ F 



Our equation (4) is by this means reduced to 



sm 9 ^ sm 9' ' 



and (I-R)sin0 = Tsin0'-2I,by (1). 



By addition 



, „ /cos'd) . ,\ „ /cos^d)' . , \ 



or 



(I-R) 



sin (p sin (p' 



or (I — R)sin^' = T sin^ 



and by (2) (I + R)cos^=T cos0' 



.•.(l-R)sin2(^'=(T + R)sin2 



I (sin2 ^'-sin2 ^)=R (sin2 ^' + sin2 0) 



^ sin 2 (^ — sin 2 (p' 

 ~ sin 2(p + sm2(p' 



tan (p — (p' 



tan (p + (p' 



